function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

hx = sigmoid(X * theta);


%Cost function with added regularization term - do not regularize theta1 parameter = theta0 in code
J = sum((-y .* log(hx)) - (1-y).* log(1-hx))/m + (sum((theta(2:end).^2)) * lambda/(2*m));


%compute partial dertivates - do not regularize theta1 parameter = theta0 in code
grad = (sum((hx-y).* X)/m)' + (lambda .* theta .* [0; ones(length(theta)-1, 1)])/m;

  

 


% =============================================================

end
